Molecular dynamics simulations are usually performed with a fixed number of particles in a periodic box of constant size and shape, however, there are situations in which it is desirable to carry out simulations, where the volume of the periodic box is allowed to fluctuate and the external pressure is fixed. The external pressure and the volume are related by a stress tensor. In this paper a novel instantaneous external stress tensor is derived, which allows the volume and the internal pressure to fluctuate in a constant external pressure simulation. Compared to other constant pressure simulation methods, the method proposed contains no artificial parameter and no extension of the phase space. It is shown that time averages of system properties are equal to isoenthalpic-isobaric ensemble averages. The implementation of the proposed method in a constant pressure molecule dynamics simulation is outlined and result of simulations of Lennard- Jones particles are presented. © 1992 Taylor and Francis Ltd.